Optimizing the Product Rule: Common Error Help for (5x-2)^3 / (2x+5)^4

[fr33pl4gu3]

y = ( 5 x-2 ) ³ / ( 2 x+5 ) ⁴

I do it this way:

f(x) = (5x-2)³
g(x) = (2x+5)^-4
f'(x) = 3(5x-2)²
g'(x) = -4(2x+5)^-5

By using the product rule:

[3(5x-2)²](2x+5)^-4 + (5x-2)³[-4(2x+5)^-5]
3(5x-2)²(2x+5)^-4 -4(2x+5)^-5(5x-2)³

What's wrong with this answer?

 

[berkeman]

Thread moved to Homework Help

f'(x) = 3(5x-2)2
g'(x) = -4(2x+5)-5

I do not believe you have differentiated correctly in these steps.

 

[fr33pl4gu3]

Is it this way??

f'(x) = 15(5x-2)²
g'(x) = -8(2x+5)^-5

 

[fr33pl4gu3]

Yes, got it. Thanks for pointing out the error.